Essential Skills - Maths

Overview

This course has been developed to align with the content and standards expected at Australian Core Skills Framework (ACSF) Level 3 in numeracy and with the competencies expected at this level in relevant units of competency from the FSK13 Foundation Skills Training Package.

Rationale

Maths impacts upon the daily life of people everywhere and helps them to understand the world in which they live and work. The Essential Skills - Maths course is designed for learners who require a structured and tightly focused course to develop their numeracy skills to the standard expected by the TCE requirement for everyday adult mathematics.

Aims

The course has been designed to enable learners to achieve the standard required by the TCE for everyday adult mathematics. Course delivery must be flexible in order to meet the needs of a range of learners and to enable them to achieve the course’s stated learning outcomes in a timeframe appropriate to their background skills and knowledge.

This course focuses on the aspects of numeracy required by the TCE standard and does not replace the study of the subject Mathematics.

Learning Outcomes

On successful completion of this course, learners will be able to:

interpret and calculate with whole numbers and familiar fractions, decimals and percentages in an everyday adult context
estimate, measure and calculate routine metric measurements in an everyday adult context
interpret, draw and construct 2D and 3D shapes in an everyday adult context
use routine maps and plans in an everyday adult context
construct routine tables and graphs in an everyday adult context
interpret routine tables, graphs and charts in an everyday adult context
use basic functions of a calculator.

Access

Access to this course is restricted to learners who cannot meet the learning outcomes before entry to the course. Providers of this course must have an assessment process to identify the level of support learners need to attain requisite levels of numeracy competence.

Pathways

This course provides the opportunity for a learner to achieve the standard required by the TCE for everyday adult mathematics. For some learners, it may provide a pathway to Workplace Maths Level 2.

Course Size And Complexity

This course has a complexity level of 2.

At Level 2, the learner is expected to carry out tasks and activities that involve a range of knowledge and skills, including some basic theoretical and/or technical knowledge and skills. Limited judgement is required, such as making an appropriate selection from a range of given rules, guidelines or procedures. VET competencies at this level are often those characteristic of an AQF Certificate II.

This course has a size value of 10.

Course Delivery

The course may be delivered in a multitude of ways and would lend itself to teaching and learning set in contexts other than the traditional maths classroom. For example parts of the course might be incorporated into a VET program. Some teachers might design a program that allows their learners to develop and demonstrate numeric competency while working on tasks other than traditional maths exercises. Examples of settings for such tasks might be project-based learning, presentations, or a journal of numeracy.

Course Content

This course comprises six (6) units. All units are compulsory.

Unit 1: Use basic functions of a calculator for problem solving, investigations and applications, including:

identifying and using the four operation keys, cancel, memory and the result key, and other necessary function keys, on calculators
calculating using whole numbers, money and routine decimals and percentages
calculating with routine fractions
applying order of operations to solve multi-step calculations
interpreting display and record results
making estimations and using them to check the reasonableness of the answer to a problem
using formal and informal mathematical language and appropriate symbolism and conventions to communicate the result of the task.

Unit 2: Interpret and calculate with whole numbers and familiar fractions, decimals and percentages in an everyday adult context, including:

interpreting and comprehending whole numbers and routine or familiar fractions, decimals and percentages
demonstrating understanding of place value by ordering numbers
performing calculations using the four basic operations (addition, subtraction, multiplication, division) which may involve a number of steps
converting between equivalent forms of fractions, decimals and percentages
applying order of operations to solve multi-step calculations
locating required numerical information to perform task
using formal and informal mathematical language and symbolism to communicate the result of the task
recognising Australian coins and notes according to value and write money as symbols up to $100
recognising and naming money amounts up to one thousand
rounding to the nearest 5 cents
performing simple and familiar calculations with money, using basic operations
making estimations to check the reasonableness of the answer to a problem.

Unit 3: Estimate, measure and calculate routine metric measurements in everyday adult situations, including:

understanding metric units and the common prefixes
selecting and interpreting measurement information in tasks and texts
identifying appropriate routine measuring equipment
using appropriate routine equipment accurately (for example, setting weight scales at zero before weighing)
making estimations to check the reasonableness of the answer to a problem
estimating routine measurements and calculating using correct units
calculating areas of squares and rectangles
performing conversions between routinely used metric units
relating a real world problem to mathematical processes
recording information using mathematical language and symbols.

Unit 4: Interpret, draw and construct 2D and 3D shapes, including:

identifying two dimensional shapes and routine three dimensional shapes in everyday objects and in different orientations
explaining the use and application of shapes
using formal and informal mathematical language and symbols to describe and compare the features of two dimensional shapes and common three dimensional shapes
identifying common angles using simple tools
estimating common angles in everyday objects
using common geometric instruments to draw two dimensional shapes
constructing routine three dimensional objects from given nets.

Unit 5: Use routine maps and plans, including:

identifying features in routine maps and plans
explaining symbols and keys in routine maps and plans
demonstrating understanding of direction and location
applying simple scale to estimate length of objects, or distance to location or object
giving and receiving directions using both formal and informal language.

Unit 6: Construct and interpret routine tables, graphs and charts, including:

identifying features of common tables, graphs and charts in predominantly familiar texts and contexts
identifying uses of different tables and graphs
identifying common types of graphs and their different uses
selecting a method to collect data, determine variables and collate information in a table
determining a suitable scale and axes, draft and draw graphs from collated data
reporting and discussing information using formal and informal mathematical language
performing calculations to interpret information
explaining how statistics can inform and persuade
identifying misleading statistical information.

Work Requirements

As the course comprises six (6) compulsory units to be delivered sequentially, a minimum of 12 hours must be spent covering the content in each unit. Providers can design the course to allow for crossover of the content allowing for elements of different units to be taught concurrently to reinforce learning outcomes.

Learners will develop a range of numeric skills, including:

• interpretation and calculation with whole numbers, familiar fractions, decimals and percentages
• using basic functions of a calculator
• estimation, measurement and calculation using routine metric units
• interpretation, drawing and constructing 2D shapes and 3D objects
• those pertaining to the construction and interpretation of maps, plans and routine tables and graphs.

Over the duration of the course, students will provide evidence by completing a minimum of two (2) major and four (4) minor assessments. These minimum requirements should be scheduled so that each of the six (6) compulsory units include one of the major or minor assessments and so that students have multiple opportunities for assessment against each of the seven (7) course criteria.

Assessment

Criterion-based assessment is a form of outcomes assessment that identifies the extent of learner achievement at an appropriate end-point of study. Although assessment – as part of the learning program – is continuous, much of it is formative, and is done to help learners identify what they need to do to attain the maximum benefit from their study of the course. Therefore, assessment for summative reporting to TASC will focus on what both teacher and learner understand to reflect end-point achievement.

The standard of achievement each learner attains on each criterion is recorded as a rating of ‘C’ (satisfactory standard) according to the outcomes specified in the standards section of the course document.

A ‘t’ notation must be used where a learner demonstrates any achievement against a criterion less than the standard specified for the ‘C’ rating. The ‘t’ notation is not described in course standards.

A ‘z’ notation is to be used where a learner provides no evidence of achievement at all.

Providers offering this course must participate in quality assurance processes specified by TASC to ensure provider validity and comparability of standards across all awards. To learn more, see TASC's quality assurance processes and assessment information.

Internal assessment of all criteria will be made by the provider. Assessment processes must gather evidence that clearly shows the match between individual learner performance, the standards of the course and the learner’s award. Providers will report the learner’s rating for each criterion to TASC.

Quality Assurance Process

The following process will be facilitated by TASC to ensure there is:

a match between the standards of achievement specified in the course and the skills and knowledge demonstrated by learners
community confidence in the integrity and meaning of the qualification.

Process – TASC will verify that the provider’s course delivery and assessment standards meet the course requirements and community expectations for fairness, integrity and validity of qualifications TASC issues. This will involve checking:

learner attendance records; and
course delivery plans (the sequence of course delivery/tasks and when assessments take place):
- assessment instruments and rubrics (the ‘rules’ or marking guide used to judge achievement)
- class records of assessment
- examples of learner work that demonstrate the use of the marking guide
- samples of current learner’s work, including that related to any work requirements articulated in the course document
- archived samples of individual learner’s work sufficient to illustrate the borderline between that judged as ‘Satisfactory Achievement and ‘Preliminary Achievement’.

This process may also include interviews with past and present learners.It will be scheduled by TASC using a risk-based approach.

Additionally, the Office of TASC may require each provider to submit bodies of learners’ work sufficient to allow an assessment against a nominated criterion or range of nominated criteria and the overall award to a review meeting organised by TASC. The work, while not necessarily fully resolved, will be assessed by the provider against the nominated assessment criterion/ia and the overall award. TASC will give each provider guidance regarding the selection of learners and the nominated criterion/ia.

Each body of learner work that providers submit to the meeting will include sufficient and appropriate material for judgements to be made about the learner’s standard of maths skills.

The review meeting will give advice about the provider’s assessment standards. Providers are expected to act on this advice.

TASC may require providers to supply further samples of individual learners’ work to determine that standards have been applied appropriately when finalising learners’ results. The nature and scope of this requirement will be risk-based.

Criteria

The assessment for Essential Skills – Maths Level 2 will be based on the degree to which the learner can:

1. demonstrate mathematical understanding
2. solve real world problems using mathematics
3. demonstrate basic arithmetic skills
4. demonstrate basic skills in measurement
5. demonstrate functional skills in geometrics and using routine maps and plans
6. demonstrate functional skills in the use and interpretation of simple tables, graphs and charts
7. use appropriate mathematical representation

Standards

Criterion 1: demonstrate mathematical understanding

The learner:

Rating C
identifies place value and uses zero as required
correctly compares and orders whole numbers, fractions and decimals
correctly converts between common fractions, decimals and percentages
recognises the relationship between operations
uses numerical or measurement information appropriately in tasks and texts
identifies main steps to complete calculations or reach a location
correctly compares the features of shapes
explains the use and application of shapes
uses visual presentation of data appropriately
interprets information in a map, chart, table or graph
recognises that statistics can inform, persuade and mislead
clarifies intended meaning of activities by asking questions which go beyond repetition and rephrasing.

Criterion 2: solve real world problems using mathematics

The learner:

Rating C
interprets and appropriately relates mathematical knowledge being learned to real life problems
locates relevant numerical or measurement information in a text
decides on steps to solve a problem
checks reasonableness of an answer against an estimate
plans and organises how to gather data to investigate
uses a calculator and relevant ICT appropriately for a range of simple mathematical computations.

Criterion 3: demonstrate basic arithmetic skills

The learner:

Rating C
accurately performs multi-step calculations using the four basic operations and the order of operations
accurately calculates with whole numbers and decimals, and uses these appropriate to context
accurately calculates simple fractions (e.g. `1/2 xx 1/4 = ?`) and percentages (e.g. `45% of 200 = ?`), and uses these appropriate to context
correctly compares and orders simple fractions, decimals and percentages
correctly rounds money figures to the nearest 5 cents
accurately adds and subtracts figures expressed as dollars/cents (e.g. `$9.50 + $12.70 = $?` or `$10.00 - $8.75 = $?`)
accurately multiplies money figures using base ten multiples (e.g. `100 xx 0.5c = $?`)
accurately calculates simple divisions involving figures expressed as money (e.g. `$100 -: 3 = $?`)
accurately calculates the solution to simple and familiar problems involving figures expressed as money (e.g. adding prices in a catalogue; calculating change from $20; keeping a record of casual hours; calculating gross pay, ‘Fred gets $25 an hour, but pays 20% tax. How much will Fred have to spend if he works 15 hours?’)

Criterion 4: demonstrate basic skills in measurement

The learner:

Rating C
correctly identifies common metric units, their prefixes (milli, centi and kilo), their common use and relationships (e.g. mm = millimetres, mm; m and km are all measures of distance; mm² is a measure of area, not a measure of distance)
correctly converts simple metric units (e.g. 120 mm = ? m)
accurately uses basic measuring instruments such as rulers, scales, dials and angle measurement tools
accurately calculates length, perimeter and area of simple shapes such as rectangles and squares
accurately calculates time intervals and simple equivalences (e.g. 2 hours less 75 minutes = ?, 265 minutes = ? hours ? minutes)
makes reasonable estimates using routine measurements (e.g. approximate distance in metres between two objects)
accurately solves basic problems involving different kinds of measurement (e.g. ‘A car travels constantly at 110 km for 1 hour, 35 minutes. How far has it travelled?’).

Criterion 5: demonstrate functional skills in geometrics and using routine maps and plans

The learner:

Rating C
correctly identifies two dimensional and routine three dimensional shapes in the real world, and can make such shapes using common instruments/given nets
correctly numbers the sides/edges, corners/vertices and flat faces of common shapes
identifies common angles using simple tools
makes reasonable estimates of angles in everyday objects
uses features, symbols and scales on simple maps and plans to answer questions about distance, direction and location
accurately applies simple scales (e.g. can reproduce a regular shape at a `1:2` scale)
accurately finds locations on a map using given co-ordinates (and vice versa) and calculates distance using given scales.

Criterion 6: demonstrate functional skills in the use and interpretation of simple tables, graphs and charts

The learner:

Rating C
correctly identifies common types and features of routine tables, graphs and charts and their uses
accurately reads information expressed in simple tables, graphs and charts (e.g. finds the time of the next bus from a bus timetable, identifies the difference between figures represented in a bar graph or finds their average)
makes simple tables and appropriate types of graphs to represent information (e.g. can create a bar graph showing the heights of 8 people or a table representing traffic flow: number of different types of vehicles at 10 minute intervals)
performs calculations to interpret information from routine tables, graphs and charts.

Criterion 7: use appropriate mathematical representation

The learner:

Rating C
gives and follows verbal and written instructions
asks questions and listens to replies
uses formal and informal written mathematical language and symbolism to communicate the result of calculations
communicates, in writing or orally, by explaining and/or describing results
records measurements accurately using suitable units
collects, organises and presents mathematical information using appropriate symbolism and conventions
chooses appropriate axes for a graph to represent the data without being misleading.

Relationship With The Australian Core Skills Framework (ACSF)

TASC recommends that providers use the ACSF to guide understanding of the appropriate levels of performance in the 5 core skills of Learning, Reading, Writing, Oral Communication and Numeracy as they relate to the course content.

Those participants aiming for an award that meets TCE standards requirements should be demonstrating the core skills at ACSF level 3 (or above) in reading and writing (to meet the everyday adult reading and writing standard) and/or in numeracy (to meet the everyday adult mathematics standard).

The performance features and sample activities of the ACSF are not in themselves equivalent to the TCE’s ‘everyday adult’ standards. Rather they are illustrative of these standards.

The performance features and sample activities of the ACSF do not replace the criteria or standards in this TASC accredited course document.

The performance features and sample activities of ACSF level 3 can be used to help teachers develop and evaluate assessment instruments and can be used to inform final (summative) assessment judgements.

See the Australian Core Skills Framework for further information.

Qualifications Available

Essential Skills – Maths Level 2 (with the award of):

SATISFACTORY ACHIEVEMENT

PRELIMINARY ACHIEVEMENT

Award Requirements

The final award will be determined by the Office of Tasmanian Assessment, Standards and Certification from 7 ratings.

The minimum requirements for an award in Essential Skills – Maths Level 2 are as follows:

Satisfactory Achievement
7 ‘C’ (satisfactory standard) ratings

Preliminary Achievement
5 ‘C’ (satisfactory standard) ratings

Course Evaluation

The Department of Education’s Curriculum Services will develop and regularly revise the curriculum. This evaluation will be informed by the experience of the course’s implementation, delivery and assessment.

In addition, stakeholders may request Curriculum Services to review a particular aspect of an accredited course.

Requests for amendments to an accredited course will be forwarded by Curriculum Services to the Office of TASC for formal consideration.

Such requests for amendment will be considered in terms of the likely improvements to the outcomes for learners, possible consequences for delivery and assessment of the course, and alignment with Australian Curriculum materials.

A course is formally analysed prior to the expiry of its accreditation as part of the process to develop specifications to guide the development of any replacement course.

Expectations Defined By National Standards

The statements of standards in this section, from the nationally agreed Common Curriculum and Assessment Framework for Languages (CCAFL), are to be used to define expectations for the meaning (nature, scope and level of demand) of relevant aspects of the sections in this document setting out course requirements, learning outcomes, the course content and standards in the assessment.

This Essential Skills – Maths course meets the requirements of units of competence from the Foundation Skills (FSK130) training package. Any references in these units to the 'workplace' should be taken to refer to ‘real life everyday adult contexts, which include but are not limited to the workplace’:

Use beginning skills with whole numbers and money up to one hundred for work (FSKNUM01)

Interpret and calculate with whole numbers and familiar fractions, decimals and percentages for work (FSKNUM14)

Estimate, measure and calculate routine metric measurements for work (FSKNUM15)

Interpret, draw and construct 2D and 3D shapes for work (FSKNUM16)

Use routine maps and plans for work (FSKNUM17)

Construct routine tables and graphs for work (FSKNUM18)

Interpret routine tables, graphs and charts for work (FSKNUM19)

Use basic functions of a calculator (FSKNUM20)

A learner who gains a qualification in this course with a Satisfactory Achievement award may reasonably expect a Registered Training Organisation with the units on its scope to grant direct recognition (Recognition of Prior Learning/credit transfer) on the basis of successful achievement in this TASC accredited course.

The relationship between Essential Skills – Maths and these units of competence is shown below.

Essential Skills - Maths Course Content

Essential Skills - Maths

Units of Competence FSK13

1. Use basic functions of a calculator for problem solving, investigations and applications, including:

identify and use the four operation keys, cancel, memory and the result key, and other necessary function keys, on calculators
calculating using whole numbers, money and routine decimals and percentages
calculating with routine fractions
applying order of operations to solve multi-step calculations
interpreting display and record results
making estimations and using them to check reasonableness of the mathematical process
using formal and informal mathematical language and appropriate symbolism and conventions to communicate the result of the task.

Use basic functions of a calculator (FSKNUM20)

2. Interpret and calculate with whole numbers and familiar fractions, decimals and percentages in an everyday adult context, including:

interpreting and comprehending whole numbers and routine or familiar fractions, decimals and percentages
demonstrating understanding of place value by ordering numbers
performing calculations using the four basic operations (addition, subtraction, multiplication, division) which may involve a number of steps
converting between equivalent forms of fractions, decimals and percentages
applying order of operations to solve multi-step calculations
locating required numerical information to perform task
using formal and informal mathematical language and symbolism to communicate the result of the task
recognising Australian coins and notes according to value and write money as symbols up to $100
recognising and naming money amounts up to one thousand
rounding to the nearest 5 cents
performing simple and familiar calculations with money, using basic operations
making estimations to check reasonableness of the answer to a problem.

Criterion 3: Demonstrate basic arithmetic skills

Interpret and calculate with whole numbers and familiar fractions, decimals and percentages for work (FSKNUM14)

Use beginning skills with whole numbers and money up to one hundred for work (FSKNUM01)

3. Estimate, measure and calculate routine metric measurements in everyday adult situations, including:

understanding metric units and the common prefixes
selecting and interpreting measurement information in tasks and texts
identifying appropriate routine measuring equipment
using appropriate routine equipment accurately (for example, setting weight scales at zero before weighing)
estimating and checking answer against estimate and relative to the task
estimating making routine measurements and calculating using correct units
calculating areas of squares and rectangles
performing conversions between routinely used metric units
relating a real world problem to mathematical processes
recording the information using mathematical language and symbols.

Criterion 4: Demonstrate basic skills in measurement

Estimate, measure and calculate routine metric measurements for work (FSKNUM15)

4. Interpret, draw and construct 2D and 3D shapes, including:

identifying two dimensional shapes and routine three dimensional shapes in everyday objects and in different orientations
explaining the use and application of shapes
using formal and informal mathematical language and symbols to describe and compare the features of two dimensional shapes and common three dimensional shapes
identifying common angles using simple tools
estimating common angles in everyday objects
using common geometric instruments to draw two dimensional shapes
constructing routine three dimensional objects from given nets.

Criterion 5: Demonstrate functional skills in geometrics and using routine maps and plans

Interpret, draw and construct 2D and 3D shapes for work (FSKNUM16)

5. Use routine maps and plans, including:

identifying features in routine maps and plans
explaining symbols and keys in routine maps and plans
demonstrating understanding of direction and location
applying simple scale to estimate length of objects, or distance to location or object
giving and receiving directions using both formal and informal language.

Criterion 5: Demonstrate functional skills in geometrics and using routine maps and plans

Use routine maps and plans for (FSKNUM17)

6. Construct and interpret routine tables, graphs and charts, including:

identifying features of common tables, graphs and charts in predominantly familiar texts and contexts
identifying uses of different tables and graphs
identifying common types of graphs and their different uses
selecting a method to collect data, determine variables and collate information in a table
determining a suitable scale and axes, draft and draw graphs from collated data
report and discuss information using formal and informal mathematical language.

Criterion 6: Demonstrate functional skills in the use and interpretation of simple tables, graphs and charts

Construct routine tables and graphs for work (FSKNUM18)

Interpret routine tables, graphs and charts for work (FSKNUM19)

Accreditation

Renewal of accreditation on 14 December 2018 for the period 1 January 2019 until 31 December 2021.

Version History

Version 1 – Accredited on 3 July 2013 for use in 2014 to 2018. This course replaces Essential Skills – Numeracy (MTN210113) that was due to expire on 31 December 2014.

Version 1.a – Removal of reference to ‘A’ ratings in ASSESSMENT section.

Version 2 - Renewal of accreditation on 14 December 2018 for the period 1 January 2019 until 31 December 2021. Amendments: clarification that the six (6) compulsory units are to be to be delivered sequentially; and addition to Quality Assurance section.

Version 3 - Renewal of accreditation on 14 July 2021 for the period 1 January 2022 until 31 December 2023. Amendment: removal of compulsory delivery order of Units.